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 A306191 T(n,k) is a triangular array read by rows.  Let S_n act on the set of size two subsets of {1,2,...,n}.  T(n,k) is the number of permutations in S_n that fix exactly k size two subsets, n >= 1, 0 <= k <= binomial(n,2). 0
 1, 0, 2, 2, 3, 0, 1, 14, 0, 9, 0, 0, 0, 1, 54, 40, 15, 0, 10, 0, 0, 0, 0, 0, 1, 304, 300, 0, 100, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1, 2260, 1638, 630, 315, 0, 105, 70, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18108, 12992, 5460, 1344, 1645, 0, 420, 0, 210, 0, 112, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The action of S_n on the 2-subsets of {1,2,...,n} is defined:  For all pi in S_n, pi({i,j}) = {pi(i),pi(j)}. LINKS EXAMPLE 1, 0,   2, 2,   3,   0,  1, 14,  0,   9,  0,   0,  0, 1, 54,  40,  15, 0,   10, 0, 0, 0,  0, 0, 1, 304, 300, 0,  100, 0,  0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1, MATHEMATICA f[list_] := Flatten[Position[list /. x_ /; x > 0 -> 1, 1]]; Level[CoefficientList[Table[n! PairGroupIndex[SymmetricGroup[n], s] /. {Table[s[i] -> 1, {i, 2, Binomial[n, 2]}]}, {n, 1, 8}],    s[1]], {2}] // Grid CROSSREFS Cf. A137482 is column 1. Sequence in context: A182631 A231728 A303545 * A290125 A307356 A091426 Adjacent sequences:  A306188 A306189 A306190 * A306192 A306193 A306194 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Jan 28 2019 STATUS approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)